That is from a textbook I go back to from time to time as a self-taught student. I wrote the whole passage out for context.

I understand everything, because it is simple and easy to read, except for two things.

1. I still can't understand at all why したappears there.

2. Is the question that the very final sentence of the passage asks an actual interrogatory sentence -- does it expect the reader to come to a conclusion, or apply their (supposed) knowledge of Japanese social customs (seniority, etc.) to answer the question? Did Hiro (Maeda?) saying dōzo have any relevance to answering that question? Or is it merely rhetorical, asking for the reader's opinion?

2. Is the question that the very final sentence of the passage asks an actual interrogatory sentence -- does it expect the reader to come to a conclusion, or apply their (supposed) knowledge of Japanese social customs (seniority, etc.) to answer the question? Did Hiro (Maeda?) saying dōzo have any relevance to answering that question? Or is it merely rhetorical, asking for the reader's opinion?

2. Is the question that the very final sentence of the passage asks an actual interrogatory sentence -- does it expect the reader to come to a conclusion, or apply their (supposed) knowledge of Japanese social customs (seniority, etc.) to answer the question? Did Hiro (Maeda?) saying dōzo have any relevance to answering that question? Or is it merely rhetorical, asking for the reader's opinion?

Hiro said "douzo" to Prof. Maeda. I think it's rhetorical.

My questions weren't of earth-shattering consequence of course, but I appreciate your taking time to shed light on them. I like your answers and as I have learned to do, I wrote them in the book on so I don't forget them.

I think that the meaning/function of “～した” is now clear to you thanks to richvh’s explanation.
Let me try to give you a “tip” to memorize it.

Try to translate this sentence into Japanese.
“Time passes”

There are many ways to do this. But the point is that what the appropriate verb to describe the passage of time is.

時間 → たつ
過ぎる
流れる
経過する

And please take a look at the last verb “経過する”. It’s a kind of stiff word. But the meaning/function of this word is exactly same as the “する” in your example sentence. We don’t say “時間がする” but when some specific amount of time is indicated, we say “1時間すると” or “2時間したら” usually only when it is followed by some fact that happens AFTER that. And it sounds more casual/informal/natural compared to “経過する”.

30分ぐらいしたころ ＝ 30分ぐらい経過したころ

Which means, in other words, the “する” can be assumed as an abbreviation of “経過する” in this kind of sentence. (This is not a matter of grammar. This is only a matter of practical usage)
Although we use this verb even in semi-official writings today, I personally think the origin of this usage was kind of colloquial. This verb "する" in Japanese is a unique word. It is sometimes used like a joker in card games (like "do" in English).

Would this “theory” be helpful for somebody? (---Well, I have no idea.)

I think that the meaning/function of “～した” is now clear to you thanks to richvh’s explanation.
Let me try to give you a “tip” to memorize it.

Try to translate this sentence into Japanese.
“Time passes”

There are many ways to do this. But the point is that what the appropriate verb to describe the passage of time is.

時間 → たつ
過ぎる
流れる
経過する

And please take a look at the last verb “経過する”. It’s a kind of stiff word. But the meaning/function of this word is exactly same as the “する” in your example sentence. We don’t say “時間がする” but when some specific amount of time is indicated, we say “1時間すると” or “2時間したら” usually only when it is followed by some fact that happens AFTER that. And it sounds more casual/informal/natural compared to “経過する”.

30分ぐらいしたころ ＝ 30分ぐらい経過したころ

Which means, in other words, the “する” can be assumed as an abbreviation of “経過する” in this kind of sentence. (This is not a matter of grammar. This is only a matter of practical usage)
Although we use this verb even in semi-official writings today, I personally think the origin of this usage was kind of colloquial. This verb "する" in Japanese is a unique word. It is sometimes used like a joker in card games (like "do" in English).

Would this “theory” be helpful for somebody? (---Well, I have no idea.)

I like your explanation too. Your examples reinforce my knowledge, and I will work through them so the concept sinks in. I'll put them in my book, too.